Celi was fluent in several languages, but his thick Sicilian accent meant that he was usually dubbed when appearing in an English language film. For example, Robert Rietti provided his voice in both Thunderball and That Man from Rio. However, in the 1981 BBC serial The Borgias, in which Celi played Rodrigo Borgia, his accent was not dubbed and he was criticised for being unintelligible and hard to follow.

During his early career, Celi was also successful as a stage actor in Argentina and Brazil, where he owned an actors' company along with the Brazilian stage greats Paulo Autran and Tonia Carrero. He directed three films in South America in the 1950s, including the Brazilian hit Tico-Tico no Fubá in 1952.

Celi was married three times. He died of a heart attack in Rome in 1986.